vector calculus 3

Find the parametric equation for the curve C of intercsetion the surfaces z=x^2 +y^2 and z = 3+2x.

Identify the curve (Why it is an ellipse on the plane z=3+2x,not circle??)

ALSO,find the equations of the projection curvees of thecruves of the curve of intersection C

(i) onto the xy-plane,
(ii) onto the plane z= -4,
(iii) onto the plane y=3.

Identify all the projection curves,.